Comparison of the UNSCEAR isodose maps for annual external exposure in Fukushima with those obtained based on the airborne monitoring surveys

In 2016, UNSCEAR published an attachment to its Fukushima 2015 White Paper, entitled"Development of isodose maps representing annual external exposure in Japan as a function of time,"in which the committee presented annual additional 1 mSv effective dose ab extra isodose lines for 1, 3, 5, 10, 30, 50 years after the accident, based on the soil deposition data of radionuclides within 100 km from FDNPP. Meanwhile, the median of the ratio, c, between the external effective dose rates and the ambient dose equivalent rates at 1 m above the ground obtained by the airborne monitoring has been established to be c~0.15. We here compare the UNSCEAR predictions with respect to estimates based on the airborne monitoring. Although both methods and data used in the two approaches are di erent, the resultant contours show relatively good agreement. However, to improve the accuracy of long-term annual effective isodose lines, feedback from continuous measurements such as airborne monitoring is important.


INTRODUCTION
In 2016, in Attachment 2 of UNSCEAR's Fukushima 2015 White Paper (hereafter referred to as Att-2) [1], as well as in animation [2], UNSCEAR published maps showing isodose lines for an annual additional effective dose of 1 mSv from external exposure in years 1, 3, 5, 10, 30 and 50 years after the Fukushima Dai-ichi Nuclear Power Plant (FDNPP) accident. UNSCEAR estimated isodose lines based on radionuclide soil deposition data obtained from soil samples collected between June 6, 2011 and July 8, 2011, within 100 km from FDNPP. The data were released by the Japanese government in 2011 [3] and were reproduced by UNSCEAR with geospatial information on a 1 km grid [4]. Att-2 provides a table (Table 2  Meanwhile, Miyazaki and Hayano [5] analyzed data from a large-scale glass-badge individual dose monitoring (with GIS information of the residents' addresses) conducted by Date City, Fukushima Prefecture, together with the airborne monitoring data collected periodically by the Japanese government, and found that the ratio c of ambient dose equivalent rate to the effective dose rate from external exposure is nearly constant between 5 and 51 months after the accident, at c ∼ 0.15 [5]. Using this relationship, it becomes possible to draw annual 1 mSv isodose lines based on the airborne monitoring data.
In this paper, we compare the 1 mSv annual isodose lines predicted by UNSCEAR, with those obtained based on the airborne monitoring for 3 and 5 years after the accident, and discuss the implications.

II. MATERIALS AND METHODS
A. Reproduction of the UNSCEAR isodose lines UNSCEAR's 1 mSv annual isodose line maps were created by using 1) the 134 Cs and 137 Cs soil deposition density data released by the Japanese government, rebuilt by UNSCEAR on a 1 km mesh in the unit of MBq m −2 , and 2) dose conversion coefficients from soil deposition density to the annual additional effective dose (Table 2 of Att-2). Since the results are shown only as maps, we calculated the annual cumulative effective dose at each 1-km grid point, and reconstructed annual isodose line of 1 mSv, 3 and 5 years after the accident (by using, respectively, the difference of 2 nd and 3 rd year cumulative dose coefficients and that of 4 th and 5 th ). The agreement was satisfactory but not perfect, due to differences in the interpolation algorithms used for each.

B. Isodose lines based on the airborne monitoring maps
On the other hand, the isodose lines based on the airborne monitoring maps were generated as follows: For the annual additional effective dose 3 (5) years after the accident, we used the 8 th (10 th ) airborne monitoring data for which the reference date of dose calculation is November 19, 2013 (November 2, 2015), as indicated in Fig. 1. By multiplying the ambient dose equivalent rateḢ * (10) (µSv/h) at each airborne monitoring grid point by the factor c = 0.15 [5], the median value of the external effective dose rate of the population living in the vicinity of the grid point was obtained.
Since the ambient dose equivalent rate 1 m above the groundḢ * (10) gradually decreased over time, we cannot simply use the dose rate on the reference date of airborne monitoring as a representative of the whole year. We therefore fitted, as shown in Fig. 1, the ratios of the ambient dose rate from the 5 th through 11 th airborne monitoring at each monitoring grid point to that from the 4 th monitoring (AM-5 through AM-11 in Fig. 1), with a model function that considers physical and environmental attenuation, Here, T 134 = 2.06 y and T 137 = 30.17 y are, respectively, the physical half lives of 134 Cs and 137 Cs, T fast (= 0.43 ± 0.01 y) and T slow (> 400 y) are the fast and slow half lives of environmental decay, and a fast (= 0.60 ± 0.01) is the fraction of the fast decaying component, and k = 2.95 is the ratio of air-kerma-rate constant of 134 Cs to 137 Cs [6]. In the fit, the pre-factor N was chosen to set the value of the model function to unity at the timing of the 4 th monitoring (t = 0.65 y).
For year 3, the function f (t) (Eq. 1) was integrated from t = 2 y to t = 3 y (shaded area A in Fig. 1) and the result was compared with the value at the reference date of the 8th airborne monitoring (red dot at y = 2.69). The correction factor for year 3 thus obtained was F = 1.05. For year 5, the integration was done from t = 4 y to t = 5 y (shaded area B in Fig. 1), which yielded a factor F = 1.03. This procedure is graphically presented in Fig. 1   being slightly greater for the 5 th year.

IV. DISCUSSION
After the FDNPP accident, an airborne monitoring method has been established and carried out regularly [7], and the ambient dose equivalent rates have been released as maps and numerical data [8]. Using the data of the large-scale individual dose monitoring conducted by Date City, Fukushima Prefecture, Miyazaki et al. [5] found that the personal dose equivalent (≈ the effective dose) monitored by glass-badges, and the ambient dose equivalent of the residential area from airborne monitoring are closely correlated. However, on a closer examination, a trend in which UNSCEAR's isodose line encloses a smaller area than that generated in the present work is evident. The reason for this small but noticeable difference can be understood by comparing the attenuation of the ambient dose rate deduced from the airborne monitoring, with that assumed in the UNSCEAR's prediction. The attenuation curve obtained by analyzing the airborne monitoring data (in red), already shown in Fig 1, is reproduced in Fig. 3. In comparison, a curve (in blue) for the attenuation of effective dose rates of representative population group calculated from the levels of deposition of radionuclides on the soil is superimposed using the parameters assumed in the UNSCEAR's prediction, as described in detail in Ref. [11]. In UNSCEAR's model, the attenuation g(t) of the effective dose rate is factorized into three parts, Here, physical(t) is the physical decay curve of 134 Cs and 137 Cs, environment(t) is the environmental attenuation with a 50-% fast component half life of 1.5 y and a 50-% slow component half life of 50 y, and location(t) is the location factor for typical adults (estimated to spend 0.6 of their time in wooden one-to-two-storey houses and 0.3 of their time at work in concrete multi-storey buildings), as described in Ref [11].
The reason for the difference of two attenuation curves can be understood by showing environment(t) and local(t) of each curve individually (Fig. 4). While Eq. 1 uses smaller T fast value and does not have local(t), which makes the curve a relatively rapid asymptote to the physical decay curve. The UNSCEAR's g(t) has two, almost the similar magnitude of relatively slow attenuation functions, which together make greater reduction. The authors deem both deposition density-todose conversion coefficient and local(t) based on the study of Chernobyl accident do not fit the Fukushima's case. Although UNSCEAR's prediction is useful for policy-makers, it is necessary to update based on the latest diachronic monitoring data continuously.

V. CONCLUSIONS
In this paper, we compared two different methods to estimate the individual external doses of the public residing in the Fukushima prefecture caused by radioactive fallout following FDNPP accident in 2011. One is the method adopted by UNSCEAR, which makes use of the official soil deposition map. The other makes use of airborne monitoring maps, together with an empirical factor c = 0.15 obtained by comparing the large-scale 'glass-badge' dosemeter measurements and the airborne surveys. Although the two are independent and are based on different data and methodologies, the resultant isodose lines for an annual additional dose of 1 mSv 3 and 5 years after the FDNPP accidents show relatively good agreement. However, to improve the accuracy of long-term annual effective isodose lines, feedback from continuous measurements such as airborne monitoring is important.